Reacting flow as an example of a boundary layer under singular external conditions

Abstract

An inviscid flow with infinite gradients at the wall poses a problem for the accompanying boundary layer that is fundamentally different from the conventional one of bounded gradients. It turns out that in both cases the external gradients do not affect the first-order boundary layer, but the unbounded gradients generate second-order corrections that are of a lower order in Reynolds number than the conventional ones. The present singularity in stagnation-point reacting flow is of an algebraic type, and the boundary-layer corrections that it generates are proportional to non-integral powers of the Reynolds number, with exponents that vanish with the rate of reaction. The present example clarifies such matters as the matching of boundary layer and singular inviscid flow, the structure and decay of the new corrections, and their ranking in comparison with the conventional second-order effects. Numerical computations illustrate the problem and give quantitative results in a few selected cases.

Higher-Order Boundary-Layer Theory

“…This limitation has been removed by Werle (l08) , who permits m and n to be different in Equation 14, yielding what we will call "separately self-similar" solutions. He gives extensive tables of the results of numerical integration of each second-order problem, as it depends upon the Falkner-Skan parameter {3 and the corresponding second order parameters.…”